Subgroups — C₂×C₄×Dic₁₀₃₃ #45683079

Order 33056.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀₃₃	C₂	1	2	yes	maximal
2	C₄×Dic₁₀₃₃	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×C₁₀₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₃₃	C₄	1	8	yes	direct product factor
5	C₂×Dic₁₀₃₃	C₂²	1	4	yes	—
6	C₂³×C₁₀₃₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₀₃₃	C₄	1	4	yes	complemented
8	C₂×C₄×C₁₀₃₃	C₂²	1	2	yes	—
9	C₂²×C₁₀₃₃	C₂×C₄	1	4	yes	—
10	C₂²×C₁₀₃₃	C₂×C₄	1	2	yes	—
11	C₂²×C₁₀₃₃	C₂³	1	1	yes	characteristic
12	C₄×C₁₀₃₃	C₂×C₄	1	4	yes	complemented
13	Dic₁₀₃₃	C₂×C₄	1	8	yes	direct product factor
14	C₂×C₁₀₃₃	C₄²	1	4	yes	complemented
15	C₂×C₁₀₃₃	C₂²×C₄	1	2	yes	—
16	C₂×C₁₀₃₃	C₂²×C₄	1	1	yes	characteristic
17	C₁₀₃₃	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₄²	—	1033	1	no	maximal, Sylow
19	C₂²×C₄	—	1033	2	no	—
20	C₂²×C₄	D₁₀₃₃	1	1	yes	characteristic
21	C₄²	—	1033	4	no	—
22	C₂³	C₂×D₁₀₃₃	1	1	yes	characteristic
23	C₂×C₄	—	1033	8	no	—
24	C₂×C₄	—	1033	4	no	—
25	C₂×C₄	Dic₁₀₃₃	1	4	yes	direct product factor
26	C₂×C₄	C₂×D₁₀₃₃	1	2	yes	—
27	C₂²	C₄×D₁₀₃₃	1	4	yes	—
28	C₂²	C₂×Dic₁₀₃₃	1	2	yes	—
29	C₂²	C₂²×D₁₀₃₃	1	1	yes	characteristic
30	C₄	—	1033	8	no	—
31	C₄	C₂×Dic₁₀₃₃	1	4	yes	direct product factor
32	C₂	C₄×Dic₁₀₃₃	1	4	yes	direct product factor
33	C₂	C₂×C₄×D₁₀₃₃	1	2	yes	—
34	C₂	C₂²×Dic₁₀₃₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₁₀₃₃
commutator, hypocenter	C₁₀₃₃	C₂×C₄²
Frattini	C₂²	C₂²×D₁₀₃₃
Fitting	C₂²×C₄×C₁₀₃₃	C₂
socle, prime radical	C₂³×C₁₀₃₃	C₂²
cosocle	C₂²×C₁₀₃₃	C₂³
LCS	G ▷ C₁₀₃₃
UCS	C₁ ◁ C₂²×C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄×Dic₁₀₃₃	C₂	direct (N × H)
4. C₂×Dic₁₀₃₃	C₄	direct (N × H)
7. C₂×C₄×C₁₀₃₃	C₄	semidirect
12. C₄×C₁₀₃₃	C₂×C₄	semidirect
13. Dic₁₀₃₃	C₂×C₄	direct (N × H)
14. C₂×C₁₀₃₃	C₄²	semidirect
17. C₁₀₃₃	C₂×C₄²	semidirect
25. C₂×C₄	Dic₁₀₃₃	direct (N × H)
31. C₄	C₂×Dic₁₀₃₃	direct (N × H)
32. C₂	C₄×Dic₁₀₃₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×Dic₁₀₃₃	2
C₄×Dic₁₀₃₃	2
C₂²×C₄×C₁₀₃₃	2
C₂×C₄²	1033

Subgroups — C2×C4×Dic1033 #45683079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₁₀₃₃ #45683079